NEW YORK – The confrontation between Khizr and Ghazala Khan, the Pakistani-American parents of a US soldier killed in Iraq, and Republican presidential nominee Donald Trump has emerged as an unexpected and potentially pivotal “flash point” in the U.S. general election campaign, a leading American newspaper said yesterday.

In a report, the New York Times said that Trump “reeled” amid a sustained campaign of criticism by the bereaved parents and a rising outcry within his own party over his rough and racially charged dismissal of the couple.

“Mr. Trump has plainly struggled to respond to the reproach of a military family who lost a child, and he has repeatedly answered the Khan family’s criticism with harsh and defensive rhetoric,” it said. “And Mr. Trump’s usual political tool kit has appeared to fail him. He earned no reprieve with his complaints that Mr. Khan had been unfair to him or with his repeated attempts to change the subject to Islamic terrorism.”

Hillary Clinton sternly reprimanded Trump, saying at a church in Cleveland, Ohio, that the billionaire businessman had answered the Khan family’s sacrifice with personal disrespect, and with disrespect for American traditions of religious tolerance.

“Mr. Khan made the ultimate sacrifice in his family, didn’t he?” Mrs. Clinton said. “And what has he heard from Donald Trump? Nothing but insults, degrading comments about Muslims, a total misunderstanding of what made our country great.”

Both parents stiffened their denunciation of Mr. Trump on Sunday, saying that he lacked the moral character and basic empathy to be president. Khizr Khan, who addressed the Democratic National Convention on Thursday, said during “Meet the Press” on NBC-TV that Trump had shown disrespect to his wife, and he accused Mr. Trump of running a campaign “of hatred, of derision, of dividing us.”

In a direct appeal to voters inclined to support Trump, Khizr Khan pleaded for the rejection of his brand of politics. He also held up Trump’s proposal for banning Muslim immigration as characteristic of a campaign that he has called bigoted and contemptuous of the Constitution.

“I implore those patriotic Americans that would probably vote for Donald Trump in November; I appeal to them not to vote for hatred, not to vote for fear-mongering,” Khizr Khan said. “Vote for unity. Vote for the goodness of this country. Vote for liberty and freedom.”

And Ghazala Khan, in an opinion article published in The Washington Post, rebuked Trump for suggesting earlier this weekend that she had not been permitted to speak at the Democratic convention. Mrs. Khan said she did not speak because she did not believe she could remain composed while talking about her son, Humayun Khan.

She continued: “Donald Trump has children whom he loves. Does he really need to wonder why I did not speak?”

Ghazala Khan said Trump was “ignorant” of Islam and criticized him for saying he had sacrificed for his country. “Donald Trump said he has made a lot of sacrifices,” Ms. Khan said. “He doesn’t know what the word sacrifice means.”

In some respects, the exchange between Trump and the Khan family echoes the June controversy in which Trump assailed a federal judge, Gonzalo P. Curiel, for his “Mexican heritage,” the Times pointed out. “By going after a military family with the language of ethnic stereotypes, Mr. Trump once again breached multiple norms of American politics and staked out ground that members of his own party are unlikely to help him defend.”

Senator Lindsey Graham, a Republican from South Carolina, said on Sunday that Trump had crossed another inviolable line. Like his comments about Curiel, Graham said, Trump’s jabs at Khizr and Ghazala Khan were entirely unacceptable. “This is going to a place where we’ve never gone before, to push back against the families of the fallen,” he said.

“There used to be some things that were sacred in American politics, that you don’t do, like criticizing the parents of a fallen soldier, even if they criticize you,” Graham continued. “If you’re going to be leader of the free world, you have to be able to accept criticism, and Mr. Trump can’t.”

Congressman Mike Coffman of Colorado, a Republican who served in combat as a Marine, also decried Trump’s remarks. Coffman, who represents a crucial swing district in the Denver suburbs, said Trump had disrespected American troops.

“Having served in Iraq, I’m deeply offended when Donald Trump fails to honor the sacrifices of all of our brave soldiers who were lost in that war,” Coffman said.

In its comments, the Times said, “It is too soon to say how severe the damage to Mr. Trump’s campaign might be, but the clash has already entangled Mr. Trump in a days-long argument with a pair of sympathetic accusers and put him on the defensive over his longstanding proposal to ban Muslims from entering the United States. Mr. Trump has downplayed the idea in recent weeks as he attempts to win over swing voters for the general election, but he has never disavowed his plan for a religious test.”

Since Thursday, Khizr Khan has mounted an extraordinary public campaign to condemn Trump for the proposal, the newspaper pointed out. He has asked Republican leaders to disavow Trump and has repeatedly characterized Trump as a person of un-redeemable callousness. And this weekend, his wife joined him as a vocal critic of Trump as well.

Trump has faltered and flailed in his response. In his first reaction, during an ABC News interview, Trump questioned why Khan’s wife did not speak alongside him at the Democratic convention, implying that she had been forbidden from doing so.

Trump also insisted in the same interview that Khan was wrong to say he had not sacrificed for his country. Trump offered his work building a business as an example of his sacrifice.

Facing mounting criticism from Democrats and Republicans, Trump released a follow-up statement on Saturday night, describing the Khans’ deceased son as a hero, but insisting that Khizr Khan had “no right” to criticize him the way he did in Philadelphia.

Trump on Sunday made a third attempt to deflect Khizr Khan’s criticism, writing on Twitter that the real issue at stake in the election was terrorism. And he continued to complain that Mr. Khan had been unfair to him.

“Captain Khan, killed 12 years ago, was a hero,” Trump wrote, “but this is about RADICAL ISLAMIC TERROR and the weakness of our “leaders” to eradicate it!”

Trump added, “I was viciously attacked by Mr. Khan at the Democratic Convention. Am I not allowed to respond? Hillary voted for the Iraq war, not me!”

On television, Trump’s campaign chairman, Paul Manafort, dismissed criticism of Trump’s comments about Mrs. Khan as a Clinton campaign talking point. He attempted to distance Trump from his plan for banning Muslims, arguing that Trump was now focused on a “geographic suspension” of immigration, rather than one based on religion.

Most Republican leaders have remained silent so far as Khizr Khan and Trump have traded barbs. The top Republicans in Congress, House Speaker Paul Ryan and Mitch McConnell, the Senate majority leader, are on record for opposing Trump’s idea for banning Muslims, but neither has spoken out about Mr. Trump’s handling of criticism from the Khans, the Times said.

The Republican vice presidential nominee, Gov. Mike Pence of Indiana, may be in a particularly awkward position, it pointed out. One of his sons is a Marine, a fact he frequently mentions on the campaign trail. “Pence’s ability to navigate a racially charged argument between Mr. Trump and a Gold Star family is emerging as his first difficult test as Mr. Trump’s running mate,” the Times said.

So far, Pence has been silent, and his aides have referred requests for comment to Trump’s campaign staff, according to the Times.

A few other prominent Republicans and national security leaders have spoken out, however, expressing dismay at Trump’s rough treatment of a family that lost its son at war.

Governor John Kasich of Ohio, a Republican who has refused to endorse Trump, said the Khan family deserved better. “There’s only one way to talk about Gold Star parents: with honor and respect,” Mr. Kasich said.

And Gen. John Allen, a retired officer who led American forces in Afghanistan and later coordinated international efforts against the Islamic State, said on ABC’s “This Week” on Sunday that Trump was endangering American troops overseas with his caustic attacks on Islam. General Allen, who spoke on behalf of Clinton at the Democratic convention, singled out Mr. Trump’s criticism of the Khan family as beyond the pale.

“These words matter, and that family was humiliated by those comments,” Gen. Allen said. “And that was unfair and a shameful thing.”